Diffusion is the process of a particle moving through a system by means of molecular motion (not by flow). This is typically described by Fick's Law,
where j is the flux of the difussing species, D is the diffusion coefficient, and c is the concentration. This equation says that the flux is proportional to the negative gradient of the concentration. To illustrate diffusion, it is common to place a drop of dye in water and watch the small drop diffuse out into the bulk system (i.e. the entire system becomes colored with the dye after a period of time). When the "drop of dye" is indistinquishable from the liquid (e.g. we place a drop of water into a glass of water), the diffusion process is refered to as self-diffusion.
The diffusion coefficient can be calculated in simulation in several methods; refer to the calculating the diffusion coefficient page for more information and examples.